Theorizing and measuring radically change in physics when using discrete vs. continuous mathemati... more Theorizing and measuring radically change in physics when using discrete vs. continuous mathematical spaces. In the 20th century, Quantum and Information Theories brought into the limelight the use of discrete observables and parameters (energy states, spin-up and down, 0 and 1 …). In these theories, the reference to discrete measurable values fundamentally contributed to knowledge construction; it similarly leads to dramatic consequences in life sciences, in particular when biological dynamics are identified with information processing. Following an early debate in physics, we briefly analyze the origin and the nature of the bias thus induced in biology, in particular in relation to the understanding of causality. We show how strong consequences have been derived from vague, common sense notions and then stress their role in cancer biology. Finally, we summarize new theoretical frames that propose different directions as for the organizing principles for biological thinking and exp...
In this text, we informally expose the mathematical analysis in [BL09] of Gould’s ideas on the in... more In this text, we informally expose the mathematical analysis in [BL09] of Gould’s ideas on the increase of “complexity” along biological evolution as a result of random paths. We also revisit some related theoretical investigations on randomness (contingency) and symmetry breakings in biology, following [LM12]. Gould made several fundamental observations on how phenotypic complexity increases on average, in a random evolution, without a bias towards an increase. Technically, we understand complexity as anti-entropy, a proper biological observable. Its increase, by symmetry changes, involves a strong form of randomness. In more usual biological terms, an increase of complexity involves new elements of biological organization and the latter are “contingent” because they are not determined by the current state of the life dynamics. 1 Randomness and Complexification in Evolution. Available energy consumption and transformation, thus entropy production, are the unavoidable physical proce...
This short text summarizes the work in biology proposed in our book, Perspectives on Organisms, w... more This short text summarizes the work in biology proposed in our book, Perspectives on Organisms, where we analyse the unity proper to organisms by looking at it from different viewpoints. We discuss the theoretical roles of biological time, complexity, theoretical symmetries, singularities and critical transitions. We explicitly borrow from the conclusions in some key chapters and introduce them by a reflection on "incompleteness", also proposed in the book. We consider that incompleteness is a fundamental notion to understand the way in which we construct knowledge. Then we will introduce an approach to biological dynamics where randomness is central to the theoretical determination: randomness does not oppose biological stability but contributes to it by variability, adaptation, and diversity. Then, evolutionary and ontogenetic trajectories are continual changes of coherence structures involving symmetry changes within an ever-changing global stability.
This short paper is meant to be an introduction to the ‘Letter to Alan Turing’ that follows it. I... more This short paper is meant to be an introduction to the ‘Letter to Alan Turing’ that follows it. It summarizes some basic ideas in information theory and very informally hints at their mathematical properties. In order to introduce Turing’s two main theoretical contributions, in Theory of Computation and in Morphogenesis (an analysis of the dynamics of forms), the fundamental divide between discrete vs. continuous structures in mathematics is presented, as it is also a divide in his scientific life. The reader who is familiar with these notions, and is convinced that they (and their differences) are relevant in the mathematical understanding of phenomena, may skip this introduction and go directly to the Letter.
Progress in biophysics and molecular biology, Jan 5, 2017
The human attempts to access, measure and organize physical phenomena have led to a manifold cons... more The human attempts to access, measure and organize physical phenomena have led to a manifold construction of mathematical and physical spaces. We will survey the evolution of geometries from Euclid to the Algebraic Geometry of the 20th century. The role of Persian/Arabic Algebra in this transition and its Western symbolic development is emphasized. In this relation, we will also discuss changes in the ontological attitudes toward mathematics and its applications. Historically, the encounter of geometric and algebraic perspectives enriched the mathematical practices and their foundations. Yet, the collapse of Euclidean certitudes, of over 2300 years, and the crisis in the mathematical analysis of the 19th century, led to the exclusion of "geometric judgments" from the foundations of Mathematics. After the success and the limits of the logico-formal analysis, it is necessary to broaden our foundational tools and re-examine the interactions with natural sciences. In particula...
Progress in biophysics and molecular biology, Jan 4, 2016
Theories organize knowledge and construct objectivity by framing observations and experiments. Th... more Theories organize knowledge and construct objectivity by framing observations and experiments. The elaboration of theoretical principles is examined in the light of the rich interactions between physics and mathematics. These two disciplines share common principles of construction of concepts and of the proper objects of inquiry. Theory construction in physics relies on mathematical symmetries that preserve the key invariants observed and proposed by such theory; these invariants buttress the idea that the objects of physics are generic and thus interchangeable and they move along specific trajectories which are uniquely determined, in classical and relativistic physics. In contrast to physics, biology is a historical science that centers on the changes that organisms experience while undergoing ontogenesis and phylogenesis. Biological objects, namely organisms, are not generic but specific; they are individuals. The incessant changes they undergo represent the breaking of symmetrie...
This provocative synthetic introduction to several research themes aims at stimulating a reflecti... more This provocative synthetic introduction to several research themes aims at stimulating a reflection on our mature science, Informatics, beyond the myths that originated it and that, today, may affect its progress. The awareness of the expressiveness and of the internal limitations of digital computing is a necessary step, within the Computer Science community, to improve the relations to other sciences, where computers are increasingly used as tools. We will briefly hint to simulations problems in Physics and discuss the still prevailing projection of our fantastic machine onto Biological and Cognitive phenomena. The conference lecture will mostly focus on §.3.
Theorizing and measuring radically change in physics when using discrete vs. continuous mathemati... more Theorizing and measuring radically change in physics when using discrete vs. continuous mathematical spaces. In the 20th century, Quantum and Information Theories brought into the limelight the use of discrete observables and parameters (energy states, spin-up and down, 0 and 1 …). In these theories, the reference to discrete measurable values fundamentally contributed to knowledge construction; it similarly leads to dramatic consequences in life sciences, in particular when biological dynamics are identified with information processing. Following an early debate in physics, we briefly analyze the origin and the nature of the bias thus induced in biology, in particular in relation to the understanding of causality. We show how strong consequences have been derived from vague, common sense notions and then stress their role in cancer biology. Finally, we summarize new theoretical frames that propose different directions as for the organizing principles for biological thinking and exp...
In this text, we informally expose the mathematical analysis in [BL09] of Gould’s ideas on the in... more In this text, we informally expose the mathematical analysis in [BL09] of Gould’s ideas on the increase of “complexity” along biological evolution as a result of random paths. We also revisit some related theoretical investigations on randomness (contingency) and symmetry breakings in biology, following [LM12]. Gould made several fundamental observations on how phenotypic complexity increases on average, in a random evolution, without a bias towards an increase. Technically, we understand complexity as anti-entropy, a proper biological observable. Its increase, by symmetry changes, involves a strong form of randomness. In more usual biological terms, an increase of complexity involves new elements of biological organization and the latter are “contingent” because they are not determined by the current state of the life dynamics. 1 Randomness and Complexification in Evolution. Available energy consumption and transformation, thus entropy production, are the unavoidable physical proce...
This short text summarizes the work in biology proposed in our book, Perspectives on Organisms, w... more This short text summarizes the work in biology proposed in our book, Perspectives on Organisms, where we analyse the unity proper to organisms by looking at it from different viewpoints. We discuss the theoretical roles of biological time, complexity, theoretical symmetries, singularities and critical transitions. We explicitly borrow from the conclusions in some key chapters and introduce them by a reflection on "incompleteness", also proposed in the book. We consider that incompleteness is a fundamental notion to understand the way in which we construct knowledge. Then we will introduce an approach to biological dynamics where randomness is central to the theoretical determination: randomness does not oppose biological stability but contributes to it by variability, adaptation, and diversity. Then, evolutionary and ontogenetic trajectories are continual changes of coherence structures involving symmetry changes within an ever-changing global stability.
This short paper is meant to be an introduction to the ‘Letter to Alan Turing’ that follows it. I... more This short paper is meant to be an introduction to the ‘Letter to Alan Turing’ that follows it. It summarizes some basic ideas in information theory and very informally hints at their mathematical properties. In order to introduce Turing’s two main theoretical contributions, in Theory of Computation and in Morphogenesis (an analysis of the dynamics of forms), the fundamental divide between discrete vs. continuous structures in mathematics is presented, as it is also a divide in his scientific life. The reader who is familiar with these notions, and is convinced that they (and their differences) are relevant in the mathematical understanding of phenomena, may skip this introduction and go directly to the Letter.
Progress in biophysics and molecular biology, Jan 5, 2017
The human attempts to access, measure and organize physical phenomena have led to a manifold cons... more The human attempts to access, measure and organize physical phenomena have led to a manifold construction of mathematical and physical spaces. We will survey the evolution of geometries from Euclid to the Algebraic Geometry of the 20th century. The role of Persian/Arabic Algebra in this transition and its Western symbolic development is emphasized. In this relation, we will also discuss changes in the ontological attitudes toward mathematics and its applications. Historically, the encounter of geometric and algebraic perspectives enriched the mathematical practices and their foundations. Yet, the collapse of Euclidean certitudes, of over 2300 years, and the crisis in the mathematical analysis of the 19th century, led to the exclusion of "geometric judgments" from the foundations of Mathematics. After the success and the limits of the logico-formal analysis, it is necessary to broaden our foundational tools and re-examine the interactions with natural sciences. In particula...
Progress in biophysics and molecular biology, Jan 4, 2016
Theories organize knowledge and construct objectivity by framing observations and experiments. Th... more Theories organize knowledge and construct objectivity by framing observations and experiments. The elaboration of theoretical principles is examined in the light of the rich interactions between physics and mathematics. These two disciplines share common principles of construction of concepts and of the proper objects of inquiry. Theory construction in physics relies on mathematical symmetries that preserve the key invariants observed and proposed by such theory; these invariants buttress the idea that the objects of physics are generic and thus interchangeable and they move along specific trajectories which are uniquely determined, in classical and relativistic physics. In contrast to physics, biology is a historical science that centers on the changes that organisms experience while undergoing ontogenesis and phylogenesis. Biological objects, namely organisms, are not generic but specific; they are individuals. The incessant changes they undergo represent the breaking of symmetrie...
This provocative synthetic introduction to several research themes aims at stimulating a reflecti... more This provocative synthetic introduction to several research themes aims at stimulating a reflection on our mature science, Informatics, beyond the myths that originated it and that, today, may affect its progress. The awareness of the expressiveness and of the internal limitations of digital computing is a necessary step, within the Computer Science community, to improve the relations to other sciences, where computers are increasingly used as tools. We will briefly hint to simulations problems in Physics and discuss the still prevailing projection of our fantastic machine onto Biological and Cognitive phenomena. The conference lecture will mostly focus on §.3.
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Papers by Giuseppe Longo